Problem: $A$ $B$ $C$ If: $ AB = 9x + 6$, $ BC = 9x + 3$, and $ AC = 27$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 6} + {9x + 3} = {27}$ Combine like terms: $ 18x + 9 = {27}$ Subtract $9$ from both sides: $ 18x = 18$ Divide both sides by $18$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $BC$ $ BC = 9({1}) + 3$ Simplify: $ {BC = 9 + 3}$ Simplify to find ${BC}$ : $ {BC = 12}$